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A337726 a(n) = (3*n+2)! * Sum_{k=0..n} 1 / (3*k+2)!. 5
1, 61, 20497, 20292031, 44317795705, 180816606476401, 1236785588298582841, 13142083661260741268467, 205016505115667563788085201, 4494781858155895668489979946725, 133764708098719455094261803214536001, 5252940087036713001551661012234828759271 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

E.g.f.: (exp(3*x/2) - 2 * sin(sqrt(3)*x/2 + Pi/6)) / (3*exp(x/2) * (1 - x^3)) = x^2/2! + 61*x^5/5! + 20497*x^8/8! + 20292031*x^11/11! + ...

a(n) = floor(c * (3*n+2)!), where c = (exp(3/2) - 2 * sin((3 * sqrt(3) + Pi) / 6))/(3 * sqrt(exp(1))) = A143821.

MATHEMATICA

Table[(3 n + 2)! Sum[1/(3 k + 2)!, {k, 0, n}], {n, 0, 11}]

Table[(3 n + 2)! SeriesCoefficient[(Exp[3 x/2] - 2 Sin[Sqrt[3] x/2 + Pi/6])/(3 Exp[x/2] (1 - x^3)), {x, 0, 3 n + 2}], {n, 0, 11}]

Table[Floor[(Exp[3/2] - 2 Sin[(3 Sqrt[3] + Pi)/6])/(3 Sqrt[Exp[1]]) (3 n + 2)!], {n, 0, 11}]

PROG

(PARI) a(n) = (3*n+2)!*sum(k=0, n, 1/(3*k+2)!); \\ Michel Marcus, Sep 17 2020

CROSSREFS

Cf. A000522, A051396, A051397, A087350, A100043, A143821, A330044, A337725, A337727, A337728, A337729, A337730.

Sequence in context: A195216 A259412 A099683 * A057998 A182384 A235008

Adjacent sequences:  A337723 A337724 A337725 * A337727 A337728 A337729

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 17 2020

STATUS

approved

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Last modified October 3 02:59 EDT 2022. Contains 357230 sequences. (Running on oeis4.)